Apparatus for solving spherical triangles.



w. FRENCH 6: 0. w FREDERICK.

APPARATUS FOR SOLVING SPHERIGAL TEIANGLES.

APPLICATION FILED JULY 1,1909. L i A. than 943,532. Patemed; Dec. 1%, law.

5 SHEETS-SHEET 1,

Fig.1.

W. FRENCH & C. W. FREDERICK.

APPARATUS FOR SOLVING SPHERIGAL TRIANGLES.

APPLICATION TILED JULY 1,1909.

Patented Dec. 14, 1909.

5 SHEETS-SHEET 2.

W. FRENCH & O. W. FREDERICK.

APPARATUS FOR SOLVING SPHERIGAL TRIANGLES.

Patented De0.14,19 09.

5 SHEETS-32111 3.

d JAM/ML M APPLICATION FILED JULY 1, 1909.

W. FRENCH & G. W. FREDERIGK. APPARATUS r012 SOLVING SPHERIG'AL TEIANGLES.

APPLICATION FILED JULY 1,1909. 943532 Patented Dec. 14, 1909.

5 SHEETS--SHEET 4. 1 36920 W. FRENCH & G. W. "FR APPARATUS FOR SOLVING SPHERIUAL 'lMMr-IGLES.

APPLIGATIOI-I FILED JULY 1, 1909 ;3 532 Patented Dec. 14, 1909.

5 SEEETSSHEET i f n W 3 DQ444306? l QM wwm L ZZ'PMMZ v WWW ygwc vj K APPARATUS FGR SOLVING SPl-IEIF'ICAL Applicafion filea July l, 1809 Serial 2%.

a l oi ilal nilml Niall-3. n. ding al flashinglull in ihe llirai'ii-l of {"olamlna. have in- (en v-i'liin now and useful iinpi' ino mean in A pai'ataa for Solving Spherical 'li'iahg les; anrl W (l0 hex-eh declare the 'lolloixiiia' to he a fall. eloal, and oxail' ilagei-ip lion of ihe invention, sueh am will enable olhei's slcilloil in Tho all to which ii appen l to maize and use llie game.

'lhis invmnion relates 0 an 1 ans: 'ior aoli'in (lll'QCi'l and sinialianooasly iho info, and Silllt l lilfiS i'ho three. sphm'ieai i involved in finding: a ship's o '0 star nights, or from. two sun as all other PlfLmli'nlS in? ifili'illllill' s for no o i G. in 1 lent No, a lo l i. "ll. Laa'le s.

enilsi the invention eonsiis in l appa '1 oh ing 5 i oi pails more fully lieieinafleri (ill and particularly poinleii out 111 a'i'ing lo l'he accoi'in an sing; i \Tl. a part of this specification in \YlllCl n; and numerals refer 0 like ill the vimws2---Figure l 21 pe olive. f

the complete insli'ainonl; Fig. 2, a .lluglullllllhlifl ClGW of the celestial sphere in 0 exp L the opei'aiion of lhe in 1 i Eli-1'1 night; l i U an g ad elevalional. view of i (he i1 train i i i} a detail View oil. one i of the \"iJ'IilOTS as: l on the right aseension circle; Fig. 5, an end View of tho parisj own in l Fig. 6 a detail sectional i new on the line 6-6 of Fig. 3; Fig. '1 z rlei'ail siile elevation of the upper VQl'UlGY shown in Fig. 3; Fig. 8 is a plan View of the horizon and altitude circles; Fig. 9, a sectional elevational view of said circles; Fig. 10, a View pai'lly in section of said circles. l but showing the altitude circle in side 'vation; Fig". 11, a detail of a \CllllOl' a (lapt- 5 ed for use in connection with said altitude uii'ele; Fig. 12 a seeliioii on the line lib-if of Fig. 11; 13 and 1%, eievaiionaland plan views, respectively. of a measuring de vice clewrihed more fully hereinafter; l ig. 15, a siitional View on. the lino 15 15 of 1 Fig. 1%; Fig. 16, is a plan View of a. portion 3 pccifioation of Letters Fa text 1 eoonociioa Willi llOlill pole; the

: calculation. The angle TRIANGLES.

of the cleelination circle; Figs. fl! and 18 details of a inarlii g \ei'niei' to he used in slid (liCl(3; and Figs. 19 and 20 riohiils of a reading" Vernier med in Wllll lhe alliladv anil cleclinaiii elem to o for the purpose of explaining the 'iiai'ldaz lLl'li'lll principles of this; deiiz'e, lr-l Q r0 equator running lllU'lll of the leai'ens; H ll t vents: the celestial the concave surface he horizon; P the zenith l i'ho earthlocal'ocl al The come! of i a oele lial .s il'iei'e; ancl M avail hocl v, for example, the sun.

1 ll iOWll lo asli'onmaei's and navij lee l 21: "ion a of a heavenly body l celestial equator on a aa-irallan oiileolmal'ion l also :i ii'ieasui'ecl l1 he pole i the allaale ii of 7 io ihe lal l'aele of "e Z M is; equal to o- 1! anfl hat the are '1 is can in other womb, since [he all'iha Z1, which the a v M 'l A, may he olai nail by ole ion; and since ll o declination Z ma he ohi'ainoil from a [Wu/Um! .l/HHHF'H". ill the lill'll'lUlk ol the place is Known. the i'lll'UiSil'lC-t (Io-" 7, (lo--71,

aml (o-l. ol lie sphm'iml i'iiangle A ma he also lnmwn; anil tlwreliore the other parts of the triangle may he asce 'lained by Z 12 1'01." example,

being has ohlainoil. and if the body .ill is lhe sun. The loval time is had. aniil from this the longilmle of {he place of Ol 5 31\'illl0ll is gotten by comparing it with lhe Greenwich time as given h cl konoinelei', all as is well known l'w navigal i'a. lal if is equally well known that he a ileulalions necny in aa'vi' aim time, that they require a amoaat of aslronoiaieal lcaoivlmlge in or fey lo he 1111Cl8 with ar'cai'aov Ul'HlQi all comlitions; and that they are often very laborious. In order t overcome these. (lifliealties I provide an instruinenl having circles eorrespontlii'ig to the that the celestial equator, to the horizon, to the ridians or declination circles, and to the tical or altitude circles or the heavens; on these circles l ver and provide i'uarkcrs wl ich are adapted to set oil or indicate the various I various parts may be- .rcad oil at once with out any cahrulations, all as will now be explained.

lleferrin more particularly to Fig. l of the drawings, 1 represents a graduated circle COLL'CSPOlltllDg to the horizon or azimuth cir cle H. 1t; 2 represents a meridian or declina tion circle corresponding to the meridian P M O; 3 an axis perpendicular to the plane of the circle 1 and the end i of which therefore corresponds to the zenith Z. While 5 is a circle perpendicular to the circle 2 and therefore corresponding to the equator or right ascension circle E For convenience of construction, the circle 5, instead of intersecting the azimuth and declination circles, as does the equator in. Fig. 2, is placed to line side of said circles, as indicated in Fig. 1,, It said circle 5 imagined,

however, as shifted toward the right in said figure, until its center coincides with the ,centenot' said circles 1 and 9 but always lying in a plane perpendicular to said circle 2, the relative positions of all the circles mentioned will be the same as in F ig. 2. The azimuth circle 1, is carried by an axis 6 pivoted in the wyes 7 carried by a yoke 8, supported on the standardl), rising from the base 10. This axis may be pictured as corresponding to the line B C in Fig. 2, and it permits the horizon or azimuth circle to swing through very large arcs. In the same way themeridian or declination circle 2 is pivoted at 11 and 12 on an axis perpezr dicular to the 6, and corresponding to the straight line joining P D in Fig. 2. The two axes just mentioned are sodisposed in i the instrument that they intersect at the common center ofthe circles which corresponds 'to the position of the earthor to the point T in Fig. 2. A little consideration will show that the point 12 on the instrument corresponds to the north pole of, the heavens, the point 11 to the south pole, and the pivots 7 to the and west points in the horiionp These four points, it will be observed, are fixed 10. Pivotally mounted on the axis 3, and

in relation to the base me- 7 rants 15 and ll constitutiu a semicircle. as

shown, and correrponding to the vertical or altitude circle 22' it I in Fig. The axis 3 there tore corresponds to the line Z T in Fig. .2, and it also passes through the common center of the circles and at right angles to the axis 6. The declination circle 2 is provided with suitable markers 17 and 18 of the wrnier type; the vertical circle 15, 16 is provided with like nun-hers 19, and the right ascension circle 5 is provided with movable \erniers 20 and 21 rigid with the declination circle 2.

it is evident from an inspection of Fig. 2, that if the declination circle P M O could he swung around the axis 1 D, and if the altitude circle Z M A could be swung around the axis Z T, while the azimuth circle could be swung around the axis B C, that any triangle corresponding to any given set of coordinates whatever could be formed. 'lhat to sayflvith the freedom of movement stated, these three particular circles could be so disposed as to cause the point of interscction of the altitude and declination circles to belocatcd in any point in the heavens whatever, and when said intersection is so'located said circles would, also,

I V. give by inspection all the other parts of the astronomical triangle. Furthermore, Fig. 2 shows that the inclination of the declination circle P M O to the altitude circle Z M A is measured by the are P Z or C0L. Therefore, itis obvious if we observe the sun,for example,and find its altitude k to be "31, we may get its true declination from the Nautical Almanac and mark it off by the appropriate Vernier l7 or 1 8 on the declination circle. We may likewise mark old said observed altitude on the altitude circle 15,

16, by the appropriate Vernier l9; and we may incline the point 4 of the axis 3 so that its distance from the polar point on the declination circle is equal to the difference between 90 and the latitude, or to G0-L. ma-11y, we may then without; disturbing this last relation move the circles 1 and? about their respective axes until each ,of the marking verniers show said circles to intersect i atthe point corresponding to the cohrdin'at/es given. After having performed these operations it isevident that the triangle Z P M in Fig. 2 will be reproduced on the instrument, and that {its hour angle Z P Mniay be read oil on the right ascen sion circle 5, sinee' it is measured by the are '0 O. From this we may get at once the local. time and the longitude of the place by comparing with a chronomilter, all in the manner well known, and without the usual calculations.

In carrying out the above operations, however, if accuracy is to be attained it is essential that the instrument be provided movable-around the same, are two quadl with certain refinements now to be described,

vided with the alidahle vernicre 19, as shown and which are not found in Patent No. 703,139 ahove. Also, if two star sights, or two sun sighte, are to he solved simultaneously, it is necessary to divide the declinaf tion circle. as well as the altitude circle, into two parte hinged together, as will appear helow, which features are likewise not; found in said patent.

In the first place, it desirable that the circle 15, 10, he capable of a slow motion and he provided with a clamp to fix it in any position to which it may be adjusted. To these ends there is provided the screws and 26 appropriately threaded and beveled at their ends, which take against. the SQClOl shaped piece 2? rigid with the axis 6. When these screws are unclampcd the altitude circle can he freely moved by hand to the approximate position, after which by setting up on one or both hcrewe a very fine micrometer adjustment may be attained. while at the me time clanipingltthe circle. Again, the adjusting screw 28 and'clamping screw 25) serve to slowly move and to accirately fir; the circle 5 in any desired position. This circle pro- Yidcd with a verifier 30, as shown, and is preferably graduated on one face with hours lotright ascension, and on the other with degrees of longitude.

The circle is provided with the rigidl; fixed arms 35 carrying the verntere 20 and 21, play ngovcr the circle and ti verniers are provided with the adiuetin crews 31 and 32, taking against suitable springs and 34 respectively. Suitable clai'nping Screws as 36 are also provided for the verniers, as best shown in Fig.

The altitude circle 15, 16 is not: ooh pro- 7 but also with thevcruiers 19 which are fixed to said circle and traverse the azimuth circle 1. Clamping screw. are also pim'itled for said verniers 1'0, the upper ends which appear at To cotuitcrlnilance the circle 2, weights 4-0 are provided, and to counterbalance the circle 1, the sector 27 provided with a weightel, Fig. 10. The plane of the of circle l5, 16. passes accurately through the center of its hinges, as illustrated, and the plane of the face of circle 1' passer accurately through the axis of its pivot 6.

In Fig. 11 is illustrated a large marker 50, extending over a quadrant, which may he placed. on the altitude circle for measuring negative altitudes, or altitudes helow thehorizou. 'Tlns marker is also usctul in clamping the quadrants l5 and 16 together when tracing a great circle course. It is provided with a suitable set screw 51, as shown.

In Fig. 13 is shown a device for measuring arcs, which We term a spherical compass, and it consists of a pair of legs 52 and53, the leg provided with a hollow rim Set, over which l l l l l l titsv the circular pivot 55 fit; having the la- 3 prrctl end 57 fitting in the slit 58 ot the run ll is evident when the wedge is rai-cd that" thc leg 5; may readily turn around its )ivot. hut when the wet 'e is down the )llllS l e will he chuupctl agaimt turning:

in order that the circle l and its. markers um l rccl v move lurid the circle a clan side-cable space 10. Fig. R, is lert hctwccn the two circles-1; and in order that the point: of llllGlHQtllOll ot the declination and a titude circles may 1.: accurately read. there i1 pro-- vidctl'the glass vernier scale (35. F1 l.) and 2t which adapted to lie llal; a at the altitude circle and to extend over the scale of the declination circle, or vice vcmt. .i. clainp tilt is vn'ovided in order tohohl the parts together.

in operation the clamps being tree, the :lol lowii'tg movement's will he posaihle among the parta. The altitude circle may roving freely in azimuth, its-2 vertical axis 3 may swing freely north and south in the nuu'idian, and the declination circle may move freely in an east and west direction. 'lhcretore, it is evident ftcr the coZBrdiuatc-- ot' a lieavcnl o-otly have been niarlied, a dime described, on the appropriate circles that the proper marlriiir' vcruicrs may he brought togcther at the ll'llltll'titKlitlllS of the appropriate circles and theilcuircd Fpherical triangle reproduced, as above stated. lint, since two nun-hers cannot occupy the same apace at the aanie time, the actual point sought cannot he had hf; a direct reading. ilherctorc, the scale or each marker is: so arranged that when two markers touch, it. will either indicate the desired point of intersection. or else ouch point will be indicated after a known correction has been applied. 'lo 'lai'tilitate the operation the in: rlqcre may he provide-til with int ur-eugaging grooves and pins To. as best shown in. Figafi and to, but any other suitable contacting pointa may be provided, if desired.

Since the spherical problems that can. he solrwl by this inatrtunei'it are endless, they will not. he treated in detail, but it. might be observed that a ship's position may he readil v ohtained with its aid by two atar sights, in the following iltfllitlt'dtk-ililt. altitudes 7L and /1 ol the stars El and iii, liig. 2, are ohaerved in the usual way, while their the linations (7 and (I, and their right asceneions are obtained from a Nautical i l Zmrmnc. lhe. ic right asccnsions also give the longitudes of the f tor the times of observation in the manner well known. The altitudes it and I1, are laid oil on the two quadrants 15 and it of the altitude circle by the nun-hers 11$); the dcclinations are laid oil on the declination circle bythe markers 17 and 18; and the longitudcs of the stars are laid off on the circle 5 by the verniers 20 and 21.

The coordinates of the two bodies of course will not be the same, and therefore it the altitude and declination circles are to aid in reproducin the two spherical triangles shown in Fig. 2, it; will be necessary for the arcs Z M, Z M, P O and P Fig. 2, to be capable of occupying different planes. To accomplish this, the declination circle 2 of the instrument is male in two parts hinged 'at 11 and 12, only the hinge 11 being shown. This enables the. vernier 2.1 to move independently oi the vernicr 20 on the circle .3, and therefore to indicate right ascensions or longitudes independently of Vernier 20. In the same way the. quadrants 15 and 16 may freely move around the axis 3 and indicate independent. altitudes. Owing to this construction, it is evident that the instrument may readily, in the manner above described, simultaneously reproduce the two triangles I Z hi. and i Z M inv Fig. 2..

When these triangles are reproduced the longitude of the ship will appear on Vernier 3t! which marks the meridian, and the latitude will be represented by the point e of the pin 3.

So far as we are aware no instrument has been heretofore proposed which will solve simultaneously two spherical triangles and thereby tind a ships position from two star sights, the latitude notbeing known. Furthermore, this instrument is capable of find-v ing a ships position from two sun sights involving the solution simultaneously of three triangles, the latitude not being known and the ship having moved in the interval between the sights. To do this we proceed in theway above described, obtaining the declinations and longitudes of the sun for the times of observation from the Nautical Almanac, and setting them ofl' on the instrument as in the case 01 said star sights. Also, we set oil the last mentioned altitude h as above. But. in the case of the first measured altitude h, we use the spherical coinpass, Fig. 13, so setting the extremities of its thatthey will subtend an are equal to C0h. Further, we set one of the vanes as 15 upon the reverse course of the ship and place one of the markers 19 on the same vane at -a distance from point 4, equal to the distance the ship has moved between the observations, as indicated by the log. This marker *ill then represent the position of the first zenith Z with reference to the second zenith Z. Now engage one extremity of the spherical compass with the marker representing the firstzenith Z, and bring the other extremity in contact with the marker representing the. suns first position M. Also, more the vane 16 whichcarries the marker representing the first measured altitude, so it will come into contact with the marker representing the suns last position M. When this is done the ships longitude at tee time of the last sight will appear an der the vernier 3G, and the latitude will be represented by the inclination of the axis 3.

it is evident that those skilled in the art may vary the details of construction and the arrangement of parts without departing from the spirit of the invention, it is therefore not desired to limit the invention to the construction shown, except as may bereqnired by the claims.

What is claimed is 1. In an apparatus for solving spherical triangles, the combination of an altitude circle in two parts hinged together and adapted to swing on an axis; an azimuth circle provided with an. axis at right angles to the axis of said altitude circle; a declination circle provided with an axis perpendicular to said last mentioned axis; a rightascension circle; and suitable marking verniers on said circles, substantially as described.

2. in an apparatus for solving spherical triangles, the'o'oinbination of an altitude circle; an azimutli circle; a declination circle formed in two parts hinged together and capable of independent movement; said circles provided with akes at right angles to each other on which they swing; a right ascension circle; and a vernier rigid with each. part of the declination circle adapted to play over said right ascension circle, substantially as described.

In an apparatus for solving spherical triangles the con'ibination of an altitude circle in two parts hinged together; an azimuth circle; a declination circle in two parts also hinged together; said circles prov ded with axes at right angles to each other t n which they swing; a right ascension circle; a mark" ing Vernier on each part of the altitude circle; a marking Vernier on each )art of the declination circle; Verniers'QO an 21 also on said declination circle adapted to independently play over the right ascension circle;

and means for imparting a slow motion to" said last named verniers, substantially-as described.

4. in an apparatus for solving spherical triangles, the combination of an altitude circle in two parts hinged together; an azimuth circle; a declination circle in two parts also hinged together; said circles provided with axes at right angles to each other on which they swing; a right ascension circle; a slid able marking vernier on each part of the altitude circle; a slidablc marking Vernier on each part of the declination circle; verniers and 21 also on said declination circle adapted to independently play over the right ascension circle; means for imparting a slow motion to said last named verniers; and means to impart a slow motion to said right ascension circle, substantially as described.

5. In an instrument for solving spherical triangles, the combination of an altitude circle comprising two quadrants hinged t0-' gether; sliding marking rerniers on said circle; an azimuth circle; verniers 19f rigid with said altitude circle and playing over said azimuth circle; said circles provided with axes at right angles to each other on which they swing; said azimuth circle; and means for imparting a slow motion to said sector, substantially as described.

6. In an instrument for solving spherical triangles, the combination of an altitude circle comprising two quadrants hinged together; sliding marking verniers, provided with grooves 75, on said circle; an azimuth a sector 27 rigid with circle; verniers l9 rigid with said altitude circle and playing over said azimuth circle; a sector 27 rigid with said azimuth circle; means for imparting a slow motion to said sector; a declination-circle; said circles provided with axes at right angles to each other on which they swing; and marking verniers 1.7, 18, on said declination circle provided with pins 76, substantially as described.

In testimony whereof, We afiix our signatures, in presence of two witnesses.

VILLARD FRENCH. 511* CHARLES 'W. FREDERICIC Witnesses:

K. L. BYRNE, A. \V. NEALE, Jr. 

